Question

High-voltage power lines are a familiar sight throughout the country. the aluminum (resistivity = 2.82 x 10-8Ï m) wire used for some of these lines has a cross-sectional area of 4.1 x 10-4 m2. what is the resistance of 8.2 kilometers of this wire?

Answer 1

The formula that relates the resistance R of a wire with the resistivity $\rho$ of the material of the wire is
$R= \frac{\rho L}{A}$
where L is the length of the wire (in our problem, $L=8.2 km=8200 m$) and A is the cross sectional area (in our problem, $A=4.1 \cdot 10^{-4} m^2$).
For the aluminim wire ($\rho =2.82 \cdot 10^{-8} \Omega \cdot m$) of the problem, the resistance is
$R= \frac{(2.82 \cdot 10^{-8}\Omega m)(8200 m)}{4.1\cdot 10^{-4}m^2}=0.564 \Omega$